I also didn't know that P. Quinctilius Varus was the governor of Syria in the last days of King Herod. I knew there was some controversy over Quirinius, who was governor there some ten years later. Quirinius is cited by Luke (in the Greek form Kurenios) as the governor in charge of the census at the time of Jesus's birth.
So, after I'm done reading up on the massacre in Germany in 9 AD, I need to read up on the controversy over trying to reconcile Matthew's and Luke's accounts of the birth of Christ.
EDIT: At the time Q. Varus was governor of Syria, Quirinius was fighting bandits in nearby Pisidia. Assuming that Luke is a usually careful historian, we might guess that Herod was dragging his feet on instituting the first census of Varus's administration (it would have been due about 9-8 BC), which might have led Varus to call in Quirinius to kick some butt and get the job done.
Later, Quirinius was also governor of Syria, and presided over another census, the record of which has (by chance) survived. So, he would be remembered for both things, as governor, and as the administrator of two regular censuses. So, this line of interpretation goes, Luke records a "folk memory" (factually incorrect) that the birth of Jesus took place when Q. was governor of Syria (actually, it was Varus); but then, he is at great pains to point out that this was the first census (taken by Q.).
Altogether, a plausible interpretation, though unprovable in the absence of any more records from antiquity.